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Properties

Label 225.6.q
Level $225$
Weight $6$
Character orbit 225.q
Rep. character $\chi_{225}(16,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1184$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 225.q (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(180\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(225, [\chi])\).

Total New Old
Modular forms 1216 1216 0
Cusp forms 1184 1184 0
Eisenstein series 32 32 0

Trace form

\( 1184 q - 3 q^{2} - 8 q^{3} + 2333 q^{4} + 112 q^{5} - 70 q^{6} - 8 q^{7} - 140 q^{8} - 68 q^{9} + O(q^{10}) \) \( 1184 q - 3 q^{2} - 8 q^{3} + 2333 q^{4} + 112 q^{5} - 70 q^{6} - 8 q^{7} - 140 q^{8} - 68 q^{9} - 80 q^{10} - 971 q^{11} - 364 q^{12} - 3 q^{13} - 1379 q^{14} - 948 q^{15} + 36413 q^{16} + 1056 q^{17} + 9780 q^{18} - 12 q^{19} - 4289 q^{20} - 5385 q^{21} - 131 q^{22} - 11279 q^{23} + 7230 q^{24} - 6616 q^{25} - 65056 q^{26} - 18353 q^{27} + 6004 q^{28} - 10095 q^{29} - 6714 q^{30} - 4437 q^{31} + 6732 q^{32} + 32245 q^{33} + 61 q^{34} + 27854 q^{35} - 17392 q^{36} + 20016 q^{37} - 67925 q^{38} - 18220 q^{39} + 4081 q^{40} - 26899 q^{41} + 210592 q^{42} - 8 q^{43} + 73204 q^{44} + 127732 q^{45} - 140 q^{46} + 5810 q^{47} + 104285 q^{48} - 1306152 q^{49} + 71427 q^{50} + 39334 q^{51} - 4195 q^{52} - 75612 q^{53} - 98737 q^{54} + 36100 q^{55} - 129720 q^{56} - 229102 q^{57} - 10163 q^{58} - 126390 q^{59} + 422187 q^{60} - 3 q^{61} - 214544 q^{62} + 127666 q^{63} - 1101644 q^{64} - 225459 q^{65} + 68206 q^{66} + 8268 q^{67} + 416244 q^{68} + 191044 q^{69} - 180106 q^{70} + 357522 q^{71} + 243224 q^{72} - 12 q^{73} + 524250 q^{74} + 78547 q^{75} + 1912 q^{76} - 99089 q^{77} + 593308 q^{78} + 89505 q^{79} + 433498 q^{80} + 568876 q^{81} + 276128 q^{82} - 297781 q^{83} - 154505 q^{84} - 37691 q^{85} - 148311 q^{86} - 555719 q^{87} - 118043 q^{88} + 48526 q^{89} + 1291097 q^{90} + 100830 q^{91} + 1182251 q^{92} + 193412 q^{93} + 86665 q^{94} - 132593 q^{95} - 383635 q^{96} + 175839 q^{97} - 1076794 q^{98} - 447140 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(225, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.